{"paper":{"title":"Approximation in Hermite spaces of smooth functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Christian Irrgeher, Friedrich Pillichshammer, Henryk Wozniakowski, Peter Kritzer","submitted_at":"2015-06-29T12:11:49Z","abstract_excerpt":"We consider $\\mathbb{L}_2$-approximation of elements of a Hermite space of analytic functions over $\\mathbb{R}^s$. The Hermite space is a weighted reproducing kernel Hilbert space of real valued functions for which the Hermite coefficients decay exponentially fast. The weights are defined in terms of two sequences $\\boldsymbol{a} = \\{a_j\\}$ and $\\boldsymbol{b} = \\{b_j\\}$ of positive real numbers. We study the $n$th minimal worst-case error $e(n,{\\rm APP}_s;\\Lambda^{{\\rm std}})$ of all algorithms that use $n$ information evaluations from the class $\\Lambda^{{\\rm std}}$ which only allows functio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08600","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}